7. Two cars A and B are moving on straight horizontal roads with constant velocities.
The velocity of A is 20 m/sec due east, the velocity of B is m/sec,
where and are unit vectors directed due east and due north, respectively.
Initially A is at the origin O, and the position vector of B is .
At time seconds, the position vectors of A and B are and , resp.

a) Find expressions for and in terms of .

b) Hence write an expression for in terms is .

We have: .

Then: .

c) Find the time when the bearing of B from A is .

Since B is always on a bearing of 45°, this occurs when: . . Then: . seconds.